The well-posedness theory for the nonlinear interaction problems between fluids and thin elastic structures (plates or shells) has seen quite a development in the last two decades. Such problems arise from various physical phenomena and they are quite challenging for various reasons. For example, the fluid domain changes in time and it depends on the displacement of the elastic structure - an unknown in the system, it is a mixed-type coupled physical system, usually there are both hyperbolic and parabolic equations in the system etc. Majority of such results use the incompressible Navier-Stokes system to model the fluid. We mention [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]} for the existence of weak solutions, and [9]}, [10]}, [11]}, [12]} for the existence of strong solutions. On the other hand, for the compressible Navier-Stokes system, there are only a handful of results which appeared in the last few years. First such result was due to Breit and Schwarzacher in [13]}, where they proved the existence of a weak solution for a shell interacting with a compressible viscous fluid. Later, Mitra proved the existence of a unique local regular solution in 2D, where the beam is viscoelastic in [14]}. Maity and Takahashi obtained a strong solution in \(L^p-L^q\)  framework for the interaction of heat-conducting fluid with a viscoelastic plate, and later Maity, Roy and Takahashi obtained a unique local regular solution in 3D [15]}, where the structure is modeled by a wave equation and doesn't have any viscosity. Trifunović and Wang obtained the existence of a weak solution in 3D in [16]}, where the structure is modeled by a nonlinear thermoelastic (or just elastic) plate, by constructing a time-continuous splitting approximation scheme that decouples the fluid and the structure.
